2(x-1)-6>-6+(x+3)-4x

2(x-1)-6>-6+(x+3)-4x

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Let's simplify this first......we have

2x - 2 - 6 > -6 + x + 3 - 4x

2x - 8 > -3 - 3x        Let's get the "x's" on the left and the "integers" on the right.... so we have

5x > 5    and

x > 1

In "interval" notation, we have (1, ∞)

To check that this is correct, pick two points on either "side" of 1......any values less than 1 should make the original inequality false, and any points greater than 1 should make it true.